Nyan-Nyan Oratorio

From MangaHelpers:
17-year-old Awaya Mugi and Yasuraoka Hanabi appear to be the ideal couple. They are both pretty popular, and they seem to suit each other well. However, outsiders don't know of the secret they share. Both Mugi and Hanabi have hopeless crushes on someone else, and they are only dating each other to soothe their loneliness. Mugi is in love with Minagawa Akane, a young teacher who used to be his home tutor. Hanabi is also in love with a teacher, a young man who has been a family friend since she was little. In each other, they find a place where they can grieve for the ones they cannot have, and they share a loneliness-driven physical intimacy. Will things stay like this for them forever?

Volume 3 contains Nyan-Nyan Oratorio:
The lonesome struggles of the only living being on Earth.